Generic Damping Functions for Propagating Importance in Link-Based Ranking

Abstract

This paper introduces a family of link-based ranking algorithms that propagate page importance through links. The algorithms include a damping function that decreases with distance, thus a direct link implies greater endorsement than a link via a longer path. PageRank is the most widely known ranking function of this family.

The main objective of this paper is to determine whether this family of ranking techniques is of some interest per se and how different choices for the damping function affect rank quality and convergence speed. Even though our results suggest that PageRank can be approximated with other, more simple forms of rankings that may be computed more efficiently, our focus is more speculative in nature, given that it aims at separating the kernel of PageRank, that is, link-based importance propagation, from the way propagation decays over paths.

We focus on three damping functions that have, respectively, linear, exponential, and hyperbolic decay on the lengths of the paths. The exponential decay corresponds to PageRank, and the other functions are new. The work we carry includes algorithms, analysis, comparisons, and experiments that study their behavior under different parameters in real web graph data.

Amongst other results, we show how to calculate a linear approximation that induces a page ordering that is almost identical to PageRank's using a fixed number of iterations. Comparisons were made using Kendall's $\tau$ on large domain datasets.